Objects, associations and subsystems: A hierarchical approach to encapsulation

We describe a compositional approach to the formal interpretation of type view diagrams and statecharts. We define theories for object instances and classes, and theories for associations between them. These theories are combined with categorical constructions to yield a formalisation of the entire system. We observe that some notations require the identification of theories intermediate between the theories of the constituent classes and associations and that of the entire system. This leads us to propose a notion of subsystem which generalises the concept of object and yields an approach to system specification employing object-like encapsulation in a nested hierarchy of components.